Quantitative Aptitude - Arithmetic Ability Questions

Rakesh goes on a trip on his motor­cycle and rides for 368 kms. If he rides for 5 hours at a speed of 49 km/hr, at what speed he travels for the remaining 3 hours of the journey?

A thief is stopped by a policeman from a distance of 150 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed of the thief as 7 km/hr and that of policeman as 9 km/hr, how far the thief would have run, before he is over- taken by the policeman?

If {12(a-b)}2+ab=p(a+b)2, then the value of p is 

A certain bank offers 8% rate of interest on the 1st year and 9% on the 2nd year in a certain fixed deposit scheme. If Rs 17,658 are received after investing for 2 years in this scheme, then what was the amount (in Rs) invested?

The points A(3,­-2), B(1,4) and C(­-2,x) are collinear. What is the value of x?

If 2 cos θ = 2 – sin θ, then what is the value of cos θ?

If a - b = 4 and ab = -3, then what is the value of a3- b3?

If a + b = 5 and ab = 6, then what is the value of a3 + b3?